I don’t know if this helps, but you can check the flixbus website for the connection from Trieste (Autostazine) to Venice airport and vice versa if they have a suitable connection for your date/time. Busses a fairly frequent and the ride itself takes a little less than two hours, tickets are around 15€ pp. When I disembarked in Trieste the last time, I walked to the bus station, which is located near the main train station. Took me around 20 minutes with a large suitcase and a backpack.